# Diversity of Structured Domains via k-Kemeny Scores

arXiv: https://arxiv.org/abs/2509.15812 · HTML: https://mlsanity.com/paper/2509.15812/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 63 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [On the Computation of Fully Proportional Representation](https://mlsanity.com/paper/1402.0580/) (2014)
- [Eliciting Single-Peaked Preferences Using Comparison Queries](https://mlsanity.com/paper/1401.3449/) (2014)
- [Preference Restrictions in Computational Social Choice: A Survey](https://mlsanity.com/paper/2205.09092/) (2022)
- [Diversity, Agreement, and Polarization in Elections](https://mlsanity.com/paper/2305.09780/) (2023)
- [Understanding Distance Measures Among Elections](https://mlsanity.com/paper/2205.00492/) (2022)
- [Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning](https://mlsanity.com/paper/2205.07831/) (2022)
- [Near-Tight Algorithms for the Chamberlin-Courant and Thiele Voting Rules](https://mlsanity.com/paper/2212.14173/) (2022)
- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [The one-dimensional Euclidean domain: Finitely many obstructions are not enough](https://mlsanity.com/paper/1506.03838/) (2015)
- [Weighted majority tournaments and Kemeny ranking with 2-dimensional Euclidean preferences](https://mlsanity.com/paper/2106.13054/) (2021)
- [Single-Peaked Opinion Updates](https://mlsanity.com/paper/2204.14094/) (2022)

## Built on by (most cited first, 2 of 2)

- [Agreement, Diversity, and Polarization Indices for Approval Elections](https://mlsanity.com/paper/2605.14983/) (2026)
- [Outer Diversity of Condorcet Domains](https://mlsanity.com/paper/2610.00720/) (2026)

## Abstract (arXiv)

In the k-Kemeny problem, we are given an ordinal election, i.e., a collection of votes ranking the candidates from best to worst, and we seek the smallest number of swaps of adjacent candidates that ensure that the election has at most k different rankings. We study this problem for a number of structured domains, including the single-peaked, single-crossing, group-separable, and Euclidean ones. We obtain two kinds of results: (1) We show that k-Kemeny remains intractable under most of these domains, even for k=2, and (2) we use k-Kemeny to rank these domains in terms of their diversity.